https://file.aiquickdraw.com/mathbot/file/17262043751852cia3zsi.jpg

determine the domain and the range of 
the function.

The graph in the image shows a function \( f \) with a few key points marked:

- \( (-2, -1) \)
- \( (-1, 4) \)
- \( (1, 2) \)

### Domain:
The domain represents all possible \( x \)-values that the function \( f \) can take. From the graph, it is clear that the function spans the interval from \( x = -2 \) to \( x = 1 \). Therefore, the domain is:

\[
\text{Domain of } f: \ [-2, 1]
\]

### Range:
The range represents all possible \( y \)-values that the function \( f \) takes. From the graph, the lowest point is \( (-2, -1) \) and the highest point is \( (-1, 4) \). Therefore, the range is:

\[
\text{Range of } f: \ [-1, 4]
\]

Would you like further clarification or details on how these intervals were determined?

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Here are 5 related questions to deepen your understanding:

1. How do you determine if a function is continuous or not from its graph?
2. Can you identify if this function has any vertical or horizontal asymptotes?
3. What are the critical points of this function, and how do they relate to the derivative?
4. How would you write the piecewise function for this graph?
5. What is the significance of the turning points on the graph of a function?

**Tip:** When analyzing graphs, it's important to carefully observe where the function starts and ends to correctly determine both the domain and range.

Determine the domain and the range of the function shown in the graph.

Learn how to determine the domain and range of a function by analyzing its graph. This problem covers key concepts related to functions, domain, and range. The graph shows a function with points (-2, -1), (-1, 4), and (1, 2), with domain [-2, 1] and range [-1, 4]. Suitable for students in Grades 8-10.

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